🧮 algebra

1. **State the problem:** We know that 50% of the children travel by bus, and this 50% corresponds to 500 children. We need to find the total number of children attending the schoo

1. The problem states that 80% of the days in April were sunny. We need to find how many days were sunny. 2. April has 30 days in total.

1. The problem asks to write the product $xy \cdot xy \cdot xy \cdot xy$ using exponents. 2. Recall the rule for exponents: when multiplying the same base, add the exponents. For e

1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 5$$ for $x$. 2. **Formula and rules:** To solve for $x$, multiply both sides of the equation by the denominator to e

1. **State the problem:** Divide the polynomial $6x^{3}+x^{2}-x+1$ by the binomial $4x-1$. 2. **Recall the division formula:** Polynomial division is similar to long division with

1. **State the problem:** Solve the equation $\sqrt{6x+1} = 9$ for $x$. 2. **Recall the formula and rule:** To solve an equation involving a square root, we square both sides to el

1. **State the problem:** Solve the equation $\sqrt{3x-2} = 5$ for $x$. 2. **Recall the formula and rules:** To solve an equation involving a square root, we square both sides to e

1. **State the problem:** We need to find an expression equivalent to $8^{-2}$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $a^{-n} =

1. **State the problem:** We are given a line segment EC with length expressed in two ways: as a sum of lengths $23 + 40$ and as an algebraic expression $2x + 10 + 2x + 11$. We nee

1. The problem is to simplify the expression $2^0$. 2. The rule for zero exponents states that for any nonzero number $a$, $a^0 = 1$.

1. **State the problem:** Solve the quadratic equation $$4x^2 + 5x - 8 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Simplify or understand the expression $\sqrt{x}$. 2. **Formula and rules:** The square root function $\sqrt{x}$ gives the number which, when multiplied by

1. **State the problem:** Evaluate the expression $$\sqrt{\left[\frac{\left(\frac{2}{5} + \frac{1}{4} \cdot \frac{8}{3} - 1\right)}{\frac{2}{5}}\right]^2 + \frac{1}{3}} + \frac{1}{

1. **State the problem:** We are given the function $y = 2^{x+3}$ and asked to fill in the values of $x+3$ and $y$ for $x$ values from $-5$ to $0$.

1. **State the problem:** Divide the polynomial $3x^{2}+x^{5}+x^{3}+47-28x$ by $x^{3}-1$. 2. **Rewrite the dividend in standard form:** Arrange terms in descending powers of $x$:

1. Stating the problem: We need to divide the polynomial $2x^{3}+3x^{2}+5x-8$ by $x^{2}+2x+3$. 2. The formula used is polynomial long division, similar to numerical long division.

1. The problem is to complete the table for the function $y=2^{x-1}$ by calculating the values of $x-1$ and $y$ for each given $x$. 2. The formula is $y=2^{x-1}$. For each $x$, fir

1. The problem is to find the equation of the graph given that it is an inverted "V" shaped graph of a negative absolute value function centered at the point $(-2, 1)$. 2. The gene

1. We are given the inequality $\left(\frac{2}{3}\right)^{x-2} > \frac{9}{4}$. We want to find the values of $x$ that satisfy this. 2. Recall that $\left(\frac{2}{3}\right)^{x-2} =

1. **State the problem:** Solve the equation $$4^x - 3 \cdot 2^{x+1} - 16 = 0$$. 2. **Rewrite the terms:** Note that $$4^x = (2^2)^x = 2^{2x}$$.

1. **State the problem:** Find the slope $m$ of the line passing through the points $(3, 11)$ and $(-9, -13)$. 2. **Formula:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1